Prob. $4\mathrm{.}4\mathrm{.}2$ p$.$ IP$-55[$Ans: $132f\frac{t^3}{s}].$

$4\mathrm{.}4\mathrm{.}2$ WP SS Video In the region just downstream of a sluice gate, the water may develop a reverse flow region as is indicated in Fig. P$4\mathrm{.}4\mathrm{.}2$ and Video V$10\mathrm{.}9.$ The velocity profile is assumed to consist of two uniform regions, one with velocity $V_a=10fps$ and the other with $V_b=3fps.$ Determine the net flowrate of water across the portion of the control surface at section $(2)$ if the channel is $20ft$ wide.

FIGURE P$4\mathrm{.}4\mathrm{.}2$